Sorting It All Out

An ascending sorted sequence of distinct values is one in which some form of a less-than operator is used to order the elements from smallest to largest. For example, the sorted sequence A, B, C, D implies that A < B, B < C and C < D. in this problem, we will give you a set of relations of the form A < B and ask you to determine whether a sorted order has been specified or not.

 

输入

Input consists of multiple problem instances. Each instance starts with a line containing two positive integers n and m. the first value indicated the number of objects to sort, where 2 <= n <= 26. The objects to be sorted will be the first n characters of the uppercase alphabet. The second value m indicates the number of relations of the form A < B which will be given in this problem instance. Next will be m lines, each containing one such relation consisting of three characters: an uppercase letter, the character "<" and a second uppercase letter. No letter will be outside the range of the first n letters of the alphabet. Values of n = m = 0 indicate end of input.

 

输出

For each problem instance, output consists of one line. This line should be one of the following three: 
Sorted sequence determined after xxx relations: yyy...y. 
Sorted sequence cannot be determined. 
Inconsistency found after xxx relations. 
where xxx is the number of relations processed at the time either a sorted sequence is determined or an inconsistency is found, whichever comes first, and yyy...y is the sorted, ascending sequence. 

 

样例输入

4 6
A<B
A<C
B<C
C<D
B<D
A<B
3 2
A<B
B<A
26 1
A<Z
0 0

 

样例输出

Sorted sequence determined after 4 relations: ABCD.
Inconsistency found after 2 relations.
Sorted sequence cannot be determined.

 

#include <bits/stdc++.h>
#define maxn 10005
using namespace std;
typedef  long long ll;
struct  Edge
{
    int v,next;
};
struct M
{
    Edge edge[maxn];
    int head[maxn];
    int cnt;
    void init()
    {
        memset(head,-1, sizeof(head));
        cnt=0;
    }
    void addedge(int u,int v)
    {
        edge[cnt].v=v;
        edge[cnt].next=head[u];
        head[u]=cnt++;
    }
}Mp;
int ind[30],n,in[30];
int Low_ans[maxn];
int Upper_ans[maxn];
set<char> se;
bool Low_Topsort()
{
    int tot=-1;
    priority_queue<int,vector<int>,greater<int> > q;
    for(int i=0;i<26;i++)
    {
        if(ind[i]==0&&se.count(i+'A')) q.push(i);
    }
    while(!q.empty())
    {
        int u=q.top();
        q.pop();
        Low_ans[++tot]=u;
        for(int i=Mp.head[u];i!=-1;i=Mp.edge[i].next)
        {
            int v=Mp.edge[i].v;
            ind[v]--;
            if(ind[v]==0) q.push(v);
        }
    }
    if(tot==se.size()-1) return true;
    else return false;
}
void Upper_Topsort()
{
    int tot=-1;
    priority_queue<int> q;
    for(int i=0;i<26;i++)
    {
        if(ind[i]==0&&se.count(i+'A')) q.push(i);
    }
    while(!q.empty())
    {
        int u=q.top();
        q.pop();
        Upper_ans[++tot]=u;
        for(int i=Mp.head[u];i!=-1;i=Mp.edge[i].next)
        {
            int v=Mp.edge[i].v;
            ind[v]--;
            if(ind[v]==0) q.push(v);
        }
    }
}
int main()
{
    int m,i;
    //freopen("in.txt","r",stdin);
    while(~scanf("%d%d",&n,&m))
    {   if(n==0&&m==0) break;
        se.clear();
        Mp.init();
        int f=0;
        int cnt=0;
        int ans[maxn]={0};
        memset(in,0, sizeof(in));
        for(int i=1;i<=m;i++)
        {
            string s;
            memset(Low_ans,0, sizeof(Low_ans));
            memset(Upper_ans,0, sizeof(Upper_ans));
            cin>>s;
            se.insert(s[0]);
            se.insert(s[2]);
            Mp.addedge(s[0]-'A',s[2]-'A');
            in[s[2]-'A']++;
            for(int i=0;i<26;i++)
            {
                ind[i]=in[i];
            }
            if(!Low_Topsort()&&!f)
            {
                f=1;
                cnt=i;
            }
            else
            {
                for(int i=0;i<26;i++)
                {
                    ind[i]=in[i];
                }
                Upper_Topsort();
                //printf("\n");
                bool flag=true;
                for(int i=0;i<se.size();i++)
                {
                    if(Low_ans[i]!=Upper_ans[i])
                    {
                        flag=false;
                        break;
                    }
                }
                if(flag&&!f&&se.size()==n)
                {
                    f=2;
                    cnt=i;
                    for(int i=0;i<se.size();i++)
                    {
                        ans[i]=Low_ans[i];
                    }
                }
            }
        }
        if(!f)
        {
            cout<<"Sorted sequence cannot be determined."<<endl;
        }
        else if(f==1)
        {
            printf("Inconsistency found after %d relations.\n",cnt);
        }
        else if(f==2)
        {
            printf("Sorted sequence determined after %d relations: ",cnt);
            for(int i=0;i<se.size();i++)
            {
                printf("%c",ans[i]+'A');
            }
            printf(".");
            printf("\n");
        }
    }
    return 0;
}